Before giving the inapproximabilty results, let us briefly explain why the matrix multiplication exponent \(2\le \omega < 2.37286\)  [1]} appears in our statements.
Perhaps counter-intuitively, our lower bounds get higher the closer \(\omega \)  gets to 2.
Roughly speaking, this is because our results follow from reductions that employ several procedures, including fast matrix multiplication, to extract these subgraphs with few short cycles from a given graph.
In any case, our results are new and meaningful for any \(2 \le \omega < 2.37286\)  (or even any \(2 \le \omega < 3\) ); the only difference is in the constants.
